Thus, to be effective, any magnetizing influence, magnetic or other wise, must be such as to exert on the molecule a couple equal to that exerted by a magnetic field equal to one-third of the resultant magnetic intensity to be produced in the sphere.
Possibilities of Modifications in Classical Electrody namics.—The fact that the positive electricity and the negative electricity in the earth, taken by themselves, produce by their rotations such enormous magnetic fields tempts us to inquire whether some slight modification in classical electrodynamics may be made which would permit a lack of complete compensation be tween the effects of the electricity of opposite sign and leave the observed magnetic field as a residual. We have already discussed one such possibility under Possibilities of a modification of laws of force between electric charges; but although the idea there involved was comparatively simple, the result was secured at the expense of conformity with the theory of relativity. By adopting a rather more radical modification of the electrodynamic laws"), but one consistent with the theory of relativity, it has been found possible to provide for a situation in which, while the laws for the fields due to negative electricity are unaltered, the modified equations demand a contribution to the magnetic field produced by the positive electricity as a result of the acceleration, rate of change of acceleration, etc., which it experiences in its rotation, a contribution non-existent in the case of the negative electricity. The superposed distributions no longer cancel as regards magnetic field and a residual is provided for. Moreover, the modification of the laws demanded for the positive electricity is a violation of the equation of continuity, so that positive electricity is gradually destroyed as a result of the rotation, with a result that the surplus negative electricity piles up until it has created a potential gra dient in the atmosphere sufficient to insure its departure into space at a rate which balances its accumulation. (See ELECTRICITY : Atmospheric.) Finally, the modification contains a provision for a difference between the force between like and unlike charges which provides for gravitation in a manner roughly analogous to that described in section Possibilities of a modification of the laws of force between electric charges.
The modifications necessary in the fundamental laws are ex tremely small in magnitude for such accelerations, etc., as are con cerned in the earth's rotation. Thus, for example, the modification in the equation of continuity corresponds to a disappearance of only o.5 per cent of the earth's mass in years, and the dif
ference between the force of attraction between like units of electricity and the force of repulsion between unlike units amounts to less than one part in The form of the modification is adjusted so as to secure the correct ratio of the magnetic field of the earth to that of the sun and to predict an almost negligibly small magnetic field for a body of laboratory dimensions rotating at the highest attainable speed. It must be remarked, however, that the value of com parison with the sun is largely diminished on account of entirely different conditions and nature of the magnetic field to be found on that body. In one form of the theory, the expression for the magnetic field as a function of the angular velocity and size of the rotating body leads to the conclusion that magnetic fields of the known order 2,000 gauss may be expected in sunspots provided that in the spots, the solar gases may be supposed in rotation with the not unreasonable peripheral speed of 8o kilometers per second.
A brief outline of the details of the theory is as follows : The electromagnetic equations, same relation to the direction of rotation as in the case of the earth, and the magnetic axis of the sun is inclined at an angle of about 5° to the axis of rotation. The magnetic axis, moreover, exhibits a rapid "secular" variation consisting of a rotation in the opposite direction to the rotation of the sun, with a period of about eight months.
generalize.
The equations corresponding to (A) — (D) are left unchanged for the fields due to negative electricity; but for the fields due to positive electricity they are generalized in the following The 4-vector pu, pic associated with (A) and (B) is replaced by a more general 4-vector S, icS,, given by where a and j3 are invariants of the Lorentzian transformation, and the P's and Q's have the values defined in (I) and (J). The additional terms in (I) and (J) destroy the equation of conti nuity, the only one appreciably operative in this respect for uni form rotation being aP. By an appropriate choice of a we can make this term give rise to a slow death of positive electricity (amounting to a loss of 0.5 per cent of the earth's mass in years) such as to leave a continually increasing surplus of nega tive which, after building up the necessary electric field, passes off continually, as the atmospheric electric current, by conduction through the atmosphere.